WASHINGTON — The US Supreme Court said Monday it will decide the constitutionality of the Federal Communications Commission’s (FCC) rules prohibiting indecent broadcasts, a major test of the agency’s ability to police the airwaves.

The case returned to the high court for the second time in three years. A divided court ruled for the FCC on narrow grounds in 2009, finding the agency’s stepped-up efforts to combat indecency were a legally permissible exercise of the agency’s administrative powers.

The case was returned Monday for an answer to the larger question of whether the FCC’s restrictions on broadcasters’ speech violates the First Amendment.

The agency took a tougher stance toward broadcasters beginning in 2004, indicating that networks could face fines for airing even fleeting uses of profanity.

One case before the court involves FOX Television broadcasts of the 2002 and 2003 Billboard Music Awards in which Cher and Nicole Richie uttered expletives. Another case involves ABC’s airing of a 2003 episode of “NYPD Blue” that depicted a woman’s naked buttocks.

The FCC found Fox was in violation of indecency prohibitions, but did not sanction the network because the programs aired before the agency’s revised policy.

FOX is a division of News Corp., which also owns Dow Jones Newswires and NewsCore.

In the “NYPD Blue” case, the agency fined 45 ABC network-owned or affiliated stations that aired the episode.

The New York-based 2nd US Circuit Court of Appeals ruled last year that the FCC rules violated broadcasters’ constitutional free-speech rights. The appeals court said the rules are so vague that they do not give broadcasters fair warning of what constitutes a violation.

The Supreme Court will hear oral arguments during its next term, which begins in October.